Carries out a 3-Level Staggered ANOVA and Estimates Variance Components
Function to undertake an ANOVA for the unbalanced triplicates from a GSC NGR or Tri-National survey. The data must be in the following order for each triplicate: Analytical Duplicate, Field Duplicate for the Analytical Duplicate Split, other Field Duplicate. The results replicate those generated by the UANOVA (Garrett and Goss, 1980) computer program. Optionally the data may be logarithmically (base 10) transformed.
a file of triplicate determinations, the order is critical, see Details below.
by default the character string for the data file name,
if a logarithmic transformation of the data is required to meet homogeneity of variance considerations (i.e. severe heteroscedasticity) set
As noted above, the order of the data is critical and must be as follows for each triplicate: Analytical Duplicate, Field Duplicate for the Analytical Duplicate Split, other Field Duplicate. The 'other Field Duplicate' is equivalent to a regular regional-coverage sample, but is at a 'Field Duplicate' site. Thus below, x[i,1] will contain the Analytical Duplicates, x[i,2] the Field Duplicates from which the Analytical Duplicates were split, and x[i,3] the other analytically unduplicated Field Duplicates. See Details in
triples.test1 for additional information.
Any less than detection limit values represented by negative values, or zeros or other numeric codes representing blanks in the data, must be removed prior to executing this function, see
NAs in the data must also be removed prior to running the
triples.aov function. This requires care as the data must be in complete triplicate sets.
Robert G. Garrett
Bainbridge, T.R., 1963. Staggered, nested designs for estimating variance components. American Society for Quality Control, Convention Transactions, pp. 93-103.
Garrett, R.G., 2013. Assessment of local spatial and analytical variability in regional geochemical surveys with a simple sampling scheme. Geochemistry: Exploration, Environment, Analysis, 13(4):349-354, doi 10.1144.geochem2011-085.
Garrett, R.G. & Goss, T.I., 1980. UANOVA: A Fortran IV program for unbalanced nested anaylsis of variance. Mathematical Geology, 6(1):35-60.
Satterthwaite, F.E., 1946. An approximate distribution of estimates of variance components. Biometrics, 2(2):110-114.
Snee, R.D., 1974. Computation and use of expected mean squares in Analysis of Variance. Journal of Quality Technology, 6(3):128-137.
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